Computer-aided engineering method and apparatus for predicting a quantitative value of a physical property at a point from waves generated by or scattered from a body

ABSTRACT

The invention relates to Computer-Aided Engineering (CAE) systems. It concerns a new methodology to predict (1) the acoustic radiation characteristics of a mechanical structure, under operational conditions, and (2) to identify the sources on a vibrating structure from measured sound pressure levels in the field. The methodology is based on a new approach to evaluate acoustic transfer vectors (ATV), based on the reciprocity principle and combined with interpolation techniques. The same methods are applicable to other vibrating energy forms which can be described by the wave equation such as electromagnetic waves.

FIELD OF THE INVENTION

This invention relates to Computer-Aided Engineering (CAE) and inparticular to a Computer-Aided Engineering (CAE) method and apparatusfor predicting a quantitative value of a physical property at a pointfrom waves generated by or scattered from a body. For example, thephysical property can be an acoustic signature of a vibrating structure.

BACKGROUND OF THE INVENTION

The acoustic performance of manufactured products is becoming anextremely important aspect in the design and development process, notonly to improve the comfort of the user of the product (e.g. passengersin a car, in an aircraft), but also to reduce the nuisance to thesurroundings (e.g. habitations close to highways or to an airport). Atypical problem may be described or represented for numerical analysisas a vibrating body surrounded by a fluid which may be assumedeffectively infinite at least as an approximation.

The concept of Acoustic Transfer Vectors (ATV's) is known [Y. K. Zhang,M.-R. Lee, P. J. Stanecki, G. M. Brown, T. E. Allen, J. W. Forbes, Z. H.Jia, “Vehicle Noise and Weight Reduction Using Panel AcousticContribution Analysis”, SAE95, Paper 95NV69].

ATV's are input-output relations between the normal structural velocityof the vibrating surface and the sound pressure level at a specificfield point (see FIG. 3). ATV's can be interpreted as an ensemble ofAcoustic Transfer Functions from the surface nodes to a single fieldpoint. As such ATV's can be measured and are a physical parameter of asystem. Literature refers sometimes to this concept as ContributionVectors or Acoustic Sensitivities.

ATV's only depend on the configuration of the acoustic domain, i.e. theshape of the vibrating body and the fluid properties controlling thesound propagation (speed of sound and density), the acoustic surfacetreatment, the frequency and the field point. They do not depend on theloading condition. The concept of ATV's, and their properties, is notnew, and has already been published in several scientific papers.

There are two computer-aided engineering processes that are key forevaluating and optimising the acoustic performance of structures: theability to predict the acoustic radiation pattern of a vibratingstructure, either from computed or measured surface vibrations (acousticradiation prediction), and the ability to recover surface vibrationsonto a vibrating structure from measured field sound pressure level. Thelatter one is sometimes the only manner to perform sourceidentification, when it is impossible to apply measurement devices ontothe structure surface (e.g. rotating tire).

These engineering processes rely on numerical analysis methods, amongstwhich the most popular are currently the various forms of the boundaryelement method (the direct mono-domain, the direct multi-domain and theindirect approaches), and the finite element method, that can beextended to handle unbounded regions, e.g. using infinite elements.Numerical analysis is well known to the skilled person, e.g. “The finiteelement method”, Zienkiewicz and Taylor, Butterworth-Heinemann, 2000;“Numerical Analysis”, Burden and Faires, Brooks/Cole, 2001; H. A.Schenck, “Improved integral formulation for acoustics radiationproblems”, J. Acoust. Soc. Am., 44, 41-58 (1981); A. D. Pierce,“Variational formulations in acoustic radiation and scattering”,Physical Acoustics, XXII, 1993.; J. P. Coyette, K. R. Fyfe, “Solutionsof elasto-acoustic problems using a variational finite element/boundaryelement technique”, Proc. of Winter Annual Meeting of ASME, SanFrancisco, 15-25 (1989).

U.S. Pat. Nos. 5,604,893 and 5,604,891 describe finite element methodsfor solving acoustic problems by using an oblate finite element. Theoblate finite element is based on a multipole expansion that describes ascattered or radiated field exterior to an oblate spheroid.

The computational cost associated with numerical methods for acousticperformance prediction is usually very large, and is linearlyproportional to:

-   -   the number of operational conditions (may be about a 100        different cases);    -   the number of frequency lines to be evaluated for obtaining a        representative response function (will typically be about 100 to        200);    -   the number of design variants to be studied.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a method andapparatus for analysing physical systems by wave theory which is moreefficient.

It is also an object of the present invention to provide a method andapparatus for analysing physical systems by wave theory which is quickerto carry out.

It is also an object of the present invention to provide a method andapparatus for analysing a physical system by wave theory which allowsrapid recalculation following design modifications to the system.

The present invention provides a method for computing a Wave TransferVector based on the reciprocity principle, comprising the steps of:simulating positioning of a monopole, omnidirectional wave energy sourceat a reference position remote from a body; computing a boundaryoscillation amplitude of the wave generated by the source at a surfaceof the body; deriving from the boundary oscillation amplitude said WaveTransfer Vector. A wave transfer vector of a body or structuresurrounded by a medium may be described by the following equation:Prop={wtv} ^(T) {Bc}where Prop is a physical property to be determined at a field pointremote from a body or structure whereby the oscillatory surface boundaryconditions of the body or structure are defined as Bc. The surfaceboundary conditions generate or scatter waves which propagate throughthe medium to the field point and determine the physical property there.The wave transfer vector may be described as an array of transferfunctions between the surface boundary conditions of a body or structureand a physical property of the medium generated at a field point. Themedium does not have to uniform, i.e. made of a uniform materials. Thefield point may be in an internal domain (within the structure) and/orin an external domain (outside the structure).

The method may be used to analyze a structure or body in a medium inwhich Helmholtz's equation applies to the propagation of waves in themedium. The oscillatory surface states of the structure or body form oneset of boundary conditions for the solution of Helmholtz's equation,e.g. at a field point.

The computing step may be carried out by a numerical method, which maycomprise one of: a finite element method; a combination of finite andinfinite element methods; a direct boundary element method; a directmulti-domain boundary element method; and an indirect boundary elementmethod. The numerical method may be carried out on a digital computingsystem. The wave source may comprise an acoustic source.

The invention also provides a method for computing an additional WaveTransfer Vector comprising the steps of:

-   -   computing at least a first and a second wave transfer vector at        a first and a second predetermined frequency, respectively,    -   computing the additional Wave Transfer Vector at a frequency        intermediate the first and second frequency by interpolation        between the first and second Wave Transfer Vectors.

A Wave Transfer Vector may be calculated or measured. The interpolationtechnique may comprise, for example, a polynomial interpolationmechanism (e.g. linear) or a spline interpolation mechanism (e.g. cubicspline) or any other suitable interpolation technique.

The invention also provides a method to compute a Modal AcousticTransfer Vector (MATV) from an acoustic transfer vector (ATV) for aalternative coordinate system defined by a set of deformed shapes of abody, comprising the steps of:

projecting the ATV into the alternative co-ordinate system. The set ofshapes may be defined by eigen-frequencies (natural frequencies ornatural modes) of the body or by Ritz vectors (which may be described asoperational modes of the system generated by applying a specificoperational state), for example. The MATV may be used to predict aresponse of the body or the effect of such a response at a referencepoint remote from the body.

The present invention also includes methods and apparatus which combinestwo or more of ATV calculation using the reciprocity principle,generation of additional ATV's by interpolation, solution of Helmhotz'sequation using MATV derived from ATV's by projecting ATV's into modalspace and generation of additional MATV's by interpolating betweenATV's.

One or more methods of the invention may support an acoustic radiationprediction engineering process, in particular but not limited toautomotive engine and powertrain noise radiation application.

One or more methods of the invention may support a modal-based acousticradiation prediction engineering process, in particular but not limitedto automotive engine and powertrain noise radiation application.

One or more methods of the invention may support an inverse numericalacoustics engineering process, in particular but not limited toautomotive engine and powertrain noise radiation application.

One or more methods of the invention may support a modal-based inversenumerical acoustics engineering process, in particular but not limitedto automotive engine and powertrain noise radiation application.

Shapes combined to build a structural response during a method of theinvention may comprise Ritz Vectors.

One or more methods of the invention may support a Ritz-vectors-basedinverse numerical acoustics engineering process, in particular but notlimited to automotive engine and powertrain noise radiation application.

One or more methods of the invention may support an evaluation ofmultiple design alternatives, with respect to the acoustic performanceprediction of vibrating structures.

One or more methods of the invention may support an evaluation ofmultiple design alternatives, with respect to the modal-based acousticperformance prediction of vibrating structures.

One or more methods of the invention may support an automatedstructural-acoustic optimization process, with the objective functionbeing the acoustic performance prediction of vibrating structures.

One or more methods of the invention may support an automatedstructural-acoustic optimization process, with the objective functionbeing the modal-based acoustic performance prediction of vibratingstructures.

The invention also provides a processing engine adapted to carry out anyof the methods of the invention.

The invention also provides a computer program product for execution ona computer, the computer program product executing any of the methodsteps of the invention.

The invention also provides a method of inputting at a near terminal arepresentation of a body and coordinates of a reference point andtransmitting these to a remote terminal running a program for executingany of the method steps of the invention, and receiving at a nearlocation an output of any of the methods. The output may comprise oneof: an ATV, an oscillation amplitude such as an acoustic pressure level,a surface vibration of the body, a revised design of at least a part ofthe body, an acoustic intensity at a field point, a radiated acousticpower, a radiation efficiency, for example. Generally, the output may bea physical value at a field point or an integral or differentialthereof, e.g. of an electric or magnetic field.

The present invention also comprises a computer system having a memoryfor computing a Wave Transfer Vector based on the reciprocity principle,comprising: means for simulating positioning of a monopole,omnidirectional wave energy source at a reference position remote from abody; means for computing a boundary oscillation amplitude of the wavegenerated by the source at a surface of the body; and means for derivingfrom the boundary oscillation amplitude said Wave Transfer Vector. TheWave Transfer Vector may be an Acoustic Transfer Vector.

The invention consists in one aspect in a new methodology todramatically speed up the evaluation of the Wave Transfer Vectors,especially Acoustic Transfer Vectors and their exploitation. Inparticular, the use of the reciprocity principle provides improvedaccuracy of the ATV's because they can be computed and stored on anelement basis and provides a reduction in computational effort, sincethe solution needs to be performed for a number of excitation vectorsequal to the number of field points of interest, instead of to thenumber of boundary nodes.

Further on, the use of efficient interpolation techniques is veryappropriate for evaluating ATV's, due to their smooth frequencydependence, and allows the restriction of their evaluation to arestricted set of master frequency lines, which are then de-coupled fromthe excitation frequency contents. This results in significant gains incomputing time and data storage space. The use of ATV's allows apractical design optimization scheme because the computer intensive task(calculation of the ATV's) is performed up front, outside of theoptimization loop (FIGS. 9 a and b).

The developed methodology results therefore in a reduction of thecomputational cost attached to acoustic performance prediction and wavetheory problems in general, making it quasi insensitive to the number ofoperational conditions, to the number of frequency lines of interest,and to the number of design variants. As such, it allows the acousticperformance prediction tool to be driven by an automated designexploration and optimisation tool.

The present invention will now be described by way of example only andwith reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of Acoustic radiation Prediction;

FIG. 2 is a schematic diagram of Inverse Numerical Acoustics;

FIG. 3 is a schematic diagram of the concept of Acoustic TransferVectors;

FIG. 4 is a schematic diagram of a direct method for evaluating AcousticTransfer Vectors. This has to be repeated n times.

FIG. 5 is a schematic diagram of a reciprocal method for evaluatingAcoustic Transfer Vectors in accordance with an embodiment of thepresent invention;

FIG. 6 is representation of a linear interpolation of an AcousticTransfer Vector in accordance with an embodiment of the presentinvention. The interpolation curve (B) is superimposed on the ATV curve(R);

FIG. 7 shows a spline interpolation of an Acoustic Transfer Vector inaccordance with an embodiment of the present invention. Theinterpolation curve (B) is superimposed on the ATV curve (R);

FIG. 8 shows an example of panel acoustic contribution analysis;

FIGS. 9A and B show flow charts of an optimization process based onATV's and MATV's respectively, in accordance with embodiments of thepresent invention;

FIG. 10 is a block diagram of an apparatus useful for performing methodsof the invention; and

FIG. 11 is a representation of a computer system for use with thepresent invention.

DEFINITIONS

Acoustic radiation prediction: is an engineering process that aims atpredicting the sound pressure level in the surrounding field of avibrating structure (see FIG. 1). Surface vibrations create acousticpressure waves that propagate to the receiver.

Inverse numerical acoustics: is an engineering process that aims atderiving the surface vibration velocity from field sound pressuremeasurements (see FIG. 2). As such, it is the inverse problem toacoustic radiation prediction.

Discretization Methods: in order to solve acoustic radiation predictionproblems and inverse numerical acoustics problems, computer models arebuilt using numerical methods. The most frequently used numericalmethods are the boundary element method (BEM) and the finite-infiniteelement method (FEM/IFEM). These methods rely upon a discretization ofthe geometrical domain (FEM/IFEM) or of its boundary (BEM) and solve,numerically, the wave equation in the frequency domain. There existssubstantial published literature concerning both theoretical andpractical aspects of these numerical methods, for some examples of whichplease see the bibliography included in this specification. The majorcomputational effort involved within the application of many suchnumerical methods concerns the solution of a large system of linearequations.

DETAILED DESCRIPTION OF THE ILLUSTRATIVE EMBODIMENTS

The present invention will mainly be described with reference toacoustic waves but the invention is not limited thereto. The conceptsunderlying the present invention may be applied to any vibrating oroscillating energy wave which can be described by wave equations. Forexample, the present invention may be applied to electromagnetic waves.The present invention preferably relies on any suitable numericalmethods for solving such equations and problems, such as the variousforms of the boundary element method (the direct mono-domain, the directmulti-domain and the indirect approaches), and the finite elementmethod, that can be extended to handle unbounded regions, e.g. usinginfinite elements.

Generally, the methods of the present invention may be applied to a bodyor structure surrounded by (external domain) or containing (internaldomain) a medium in which waves, generated or scattered by surfacestates of the structure or body are propagated. The medium does not haveto be uniform. One example of such a physical system is a vibratingstructure surrounded by a medium such as air. Acoustic performanceprediction is applied to many different kinds of products, in a processthat is well standardised. As an example, let us consider an automotivepowertrain structure, whose goal is to minimise the acoustic soundemission, and try to quantify the benefit due to the invention.

The following is a typical practical problem. A reasonable boundaryelement model will include about 7000 nodes/elements. It should beanalysed under 50 different operating conditions, corresponding todifferent engine speed (RPM's). For building a full frequency response,about 200 frequency lines need to be computed. The performance at 10microphone locations is of interest, for example to evaluate theradiated sound power (according to the ISO3744-1981 procedure).

The computational cost for processing such a model on an engineeringworkstation is based on following figures: the matrix assembly andfactorisation process takes 5,400 seconds per frequency, and theback-substitution process (needed for each excitation case) takes 3seconds per frequency. Assuming that about 20 different designalternatives need to be analysed in the design exploration process, thefollowing estimations are obtained:

-   -   Using the traditional acoustic prediction technique (see FIG. 1)        the total computational effort can be estimated to be the number        of frequency lines (200) times the time for a single frequency        analysis (5,400 sec+3 sec×50 load cases), times the number of        design alternatives (20), i.e. 22.2 million seconds,        corresponding to 257 computing days Using the Acoustic Transfer        Vectors technique (FIGS. 3 and 4), computed in a direct way, the        model has to be solved for a number of excitation cases equal to        the number of nodes (7000), but since the exploitation time        (scalar product) is neglectible, the total computational cost is        independent of the number of design alternatives, and of        operating conditions. Therefore, the total computational effort        is estimated to be the number of frequency lines (200) times the        time for a single frequency analysis (5,400 sec+3 sec×7000        right-hand-side vectors) i.e. 5.28 million seconds,        corresponding to 61 computing days.    -   Using an embodiment of the present invention, i.e. an Acoustic        Transfer Vectors technique computed in the reciprocal manner        (FIG. 5 onwards) combined with an interpolation technique with        10 master frequencies, and neglecting the time for ATV        interpolation and exploitation, the total computational effort        can be estimated to be the number of master frequency lines (10)        times the time for a single frequency analysis (5,400 sec+3        sec×10 load cases), i.e. 54,300 seconds, corresponding to 0.6        computing days.

This example shows that, given the above assumptions, the presentinvention leads to a reduction of the computational effort by a factorof 100 compared to the conventional ATV approach, and 400 compared tothe traditional acoustic radiation prediction technique.

Theoretical background Notations A, B, H, Q Fluid domain matrixoperators ATV Acoustic Transfer Vector ATM Acoustic Transfer Matrix CSound velocity C Coupling matrix G Green's function F Frequency K Wavenumber K, D, M Fluid stiffness, damping and mass matrix operators JImaginary number N Surface normal P Acoustic pressure p_(b) Boundaryacoustic pressure S Surface of the vibrating (emitting) structure U, VComplex matrices (SVD) V Acoustic particle velocity v_(b) Boundarystructural velocity v_(s) Structural velocity x Observation point ySource point β acoustic admittance (complex) p mass density (complex) σSingle layer potential; singular values μ Double layer potential ωCircular frequency i Internal degrees of freedom (superscript) jInterface degrees of freedom (superscript)Governing Equation

Acoustic wave propagation in bounded or unbounded regions is governed bythe wave equation. Assuming an harmonic behaviour, the time and spacevariables may be separated, leading to Helmholtz' equation:∇² p+k ² p=0where k is the wave number ω/c.

Four numerical formulations are typically available for solvingHelmholtz equation over a region bounded by a surface S, with properboundary conditions, and to build Acoustic Transfer Vectors in animproved way following the principles of the invention. Each of thesemethods may be implemented on a digital computing system by theappropriate software complied to execute on the computing system,especially by using numerixcal analysis.

-   1. The direct boundary element method (DBEM) formulation, using the    acoustic pressure and velocity as boundary variables. This    formulation can be used to model homogeneous interior or exterior    domains.-   2. The multi-domain direct boundary element method (MDDBEM)    formulation, using the acoustic pressure and velocity as boundary    variables. This formulation can be used to model a non-homogeneous    domain by dividing it into a set of homogeneous sub-domains that are    linked together by continuity conditions.-   3. The indirect boundary element method (IBEM) formulation, using    the single and double layer potentials (acoustic velocity jump and    pressure jump respectively) as boundary variables. This formulation    can be used to model a homogeneous domain, where both sides of the    boundary radiate. In particular, it can be used to model an interior    domain, an exterior domain or both simultaneously.-   4. The acoustic finite/infinite element method (FEM) formulation,    using the acoustic pressure as boundary variables. This formulation    can be used to model a non-homogeneous interior domain, an exterior    domain or both simultaneously.    Direct Boundary Element Method (DBEM) Formulation

Using the DBEM formulation, the acoustic pressure at any point of ahomogeneous fluid domain containing no acoustic source can be expressedin terms of the acoustic pressure on the boundary domain and its normalderivative [see H. A. Schenk, “Improved integral formulation foracoustics radiation problems”, J. Acoust. Soc. AM. 44, 41-58 (1981)]:$\begin{matrix}{{p\left( \overset{\rightarrow}{x} \right)} = {{\int_{S}{{p\left( \overset{\rightarrow}{y} \right)}\frac{\partial{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{\partial n_{y}}{\mathbb{d}S_{y}}}} - {\int_{S}{\frac{\partial{p\left( \overset{\rightarrow}{y} \right)}}{\partial n_{y}}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}{\mathbb{d}S_{y}}}}}} & (1)\end{matrix}$where p({right arrow over (y)}) is the acoustic pressure on the boundaryand$\frac{\partial{p\left( \overset{\rightarrow}{y} \right)}}{\partial n_{y}}$its normal derivative, {right arrow over (n)}_(y) is the inward normalat point {right arrow over (y)} on the boundary and G({right arrow over(x)}|{right arrow over (y)}) is the Green's function. Making use of theEuler equation, equation (1) becomes: $\begin{matrix}{{p\left( \overset{\rightarrow}{x} \right)} = {{\int_{S}{{p\left( \overset{\rightarrow}{y} \right)}\frac{\partial{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{\partial n_{y}}{\mathbb{d}S_{y}}}} + {{j\rho\omega}{\int_{S}{{v\left( \overset{\rightarrow}{y} \right)}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}{\mathbb{d}S_{y}}}}}}} & (2)\end{matrix}$where v({right arrow over (y)}) is the normal acoustic velocity on theboundary, ρ is the fluid mass density and ω is the angular frequency.Note that the boundary acoustic velocity is related to the structuralvelocity through the following relationship:v({right arrow over (y)})=v _(s)({right arrow over (y)})+β({right arrowover (y)})p({right arrow over (y)})  (3)where v_(s)({right arrow over (y)}) is the structural velocity andβ({right arrow over (y)}) the boundary admittance. Using equation (3),equation (2) becomes $\begin{matrix}{{p\left( \overset{\rightarrow}{x} \right)} = {{\int_{S}{{p\left( \overset{\rightarrow}{y} \right)}\frac{\partial{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{\partial n_{y}}{\mathbb{d}S_{y}}}} + {{j\rho\omega}{\int_{S}{{\beta\left( \overset{\rightarrow}{y} \right)}{p\left( \overset{\rightarrow}{y} \right)}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}{\mathbb{d}S_{y}}}}} + {{j\rho\omega}{\int_{S}{{v_{s}\left( \overset{\rightarrow}{y} \right)}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}{\mathbb{d}S_{y}}}}}}} & (4)\end{matrix}$This equation is true in the domain and on its boundary. Nevertheless,when evaluated on the boundary, the Green's function and its normalderivative become singular. Whereas the last two integrals of equation(4) are regular, the first one is singular and should be evaluated inthe Cauchy's principal value sense: $\begin{matrix}{{{c\left( \overset{\rightarrow}{x} \right)}{p\left( \overset{\rightarrow}{x} \right)}} = {{P.V.{\int_{S}{{p\left( \overset{\rightarrow}{y} \right)}\frac{\partial{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{\partial n_{y}}{\mathbb{d}S_{y}}}}} + {{j\rho\omega}{\int_{S}{{\beta\left( \overset{\rightarrow}{y} \right)}{p\left( \overset{\rightarrow}{y} \right)}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}{\mathbb{d}S_{y}}}}} + {{j\rho\omega}{\int_{S}{{v_{s}\left( \overset{\rightarrow}{y} \right)}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}{\mathbb{d}S_{y}}}}}}} & (5)\end{matrix}$where $\begin{matrix}{{c\left( \overset{\rightarrow}{x} \right)} = {1 + {P.V.{\int_{S}{\frac{1}{4\pi{{\overset{\rightarrow}{x} - \overset{\rightarrow}{y}}}}\frac{\partial{{\overset{\rightarrow}{x} - \overset{\rightarrow}{y}}}}{\partial n_{y}}{\mathbb{d}S_{y}}}}}}} & (6)\end{matrix}$in the three dimensional space. Note that c({right arrow over (x)})=½for a smooth surface around {right arrow over (x)}.

Once discretized using boundary elements and evaluated at the meshnodes, equation (5) leads to the following matrix system:[A]{p _(b) }=[B]{v _(b)}  (7)where the subscript b stands for boundary. Similarly, equation (4)gives: p={d} ^(T) {P _(b) }+{m} ^(T) {v _(b)}  (8)Combining equations (7) and (8) leads to:p={atv} ^(T) {v _(b)}  (9)where {atv} is the Acoustic Transfer Vector, given by:{atv} ^(T) ={d} ^(T) [A] ⁻¹ [B]+{m} ^(T)  (10)The Acoustic Transfer Vector (ATV) is therefore an array of transferfunctions between the surface normal velocity and the pressure at thefield point. Finally, when the pressure is evaluated at severallocations, equation (9) can be rewritten as:{p}=[ATM] ^(T) {v _(b)}  (11)where the Acoustic Transfer Matrix [ATM] is formed by the differentAcoustic Transfer Vectors.

More generally, a generalised wave transfer vector of a body orstructure surrounded by a medium (external domain) or containing amedium (internal domain) may be described by the following equation:Prop={wtv} ^(T) {Bc}where Prop is a quantitative value of a physical property to bedetermined at a field point remote from a body or structure whereby theoscillatory surface boundary conditions of the body or structure aredefined as Bc. The boundary conditions may be Dirichlet, Neumann orRobin boundary conditions. The surface boundary conditions generate orscatter waves which propagate through the medium to the field point anddetermine the physical property there. The wave transfer vector may bedescribed as an array of transfer functions between the surface boundaryconditions of a body or structure and a physical property of the mediumgenerated at a field point. The waves may be any waves which can bedescribed by Helmholtz's equation, e.g. acoustic waves or, for example,electromagnetic waves scattered from an object or generated by anantenna. The medium surrounding the body does not have to be uniform.

The principles of Wave Transfer Vectors and ATV's described above may beapplied to any of the further embodiments described below.

Multi-Domain Direct Boundary Element Method (MDDBEM) Formulation

In case the acoustic region includes partitions characterised withdifferent fluid material properties, the above formulation cannot bedirectly used since it is only valid for homogeneous domains. In suchcases, a multi-domain integral formulation has to be used. The globalacoustic region is then decomposed into sub-domains with the requirementthat, within a sub-domain, the fluid properties need to be homogeneous.At the interface between the sub-domains, continuity conditions areenforced.

For sake of simplicity, let's consider here a two-domain model. Equation(7) for the first sub-domain can be written as: $\begin{matrix}{{\begin{bmatrix}A_{1}^{ii} & A_{1}^{ij} \\A_{1}^{ji} & A_{1}^{jj}\end{bmatrix}\begin{Bmatrix}p_{1}^{i} \\p_{1}^{j}\end{Bmatrix}} = {\begin{bmatrix}B_{1}^{ii} & B_{1}^{ij} \\B_{1}^{ji} & B_{1}^{jj}\end{bmatrix}\begin{Bmatrix}v_{1}^{i} \\v_{1}^{j}\end{Bmatrix}}} & (12)\end{matrix}$where superscript i stands for internal degrees of freedom andsuperscript j stands for interface degrees of freedom. Similarly,equation (7) can be rewritten for the second sub-domain as:$\begin{matrix}{{\begin{bmatrix}A_{2}^{ii} & A_{2}^{ij} \\A_{2}^{ji} & A_{2}^{jj}\end{bmatrix}\begin{Bmatrix}p_{2}^{i} \\p_{2}^{j}\end{Bmatrix}} = {\begin{bmatrix}B_{2}^{ii} & B_{2}^{ij} \\B_{2}^{ji} & B_{2}^{jj}\end{bmatrix}\begin{Bmatrix}v_{2}^{i} \\v_{2}^{j}\end{Bmatrix}}} & (13)\end{matrix}$The continuity of the normal velocity and acoustic pressure has to besatisfied at the interface between of the two sub-domains:$\begin{matrix}\left\{ \begin{matrix}{v_{1}^{j} = {{- v_{2}^{j}} = v^{j}}} \\{p_{1}^{j} = {p_{2}^{j} = p^{j}}}\end{matrix} \right. & (14)\end{matrix}$Combining equations (12), (13) and (14) leads to the global system ofequations: $\begin{matrix}{{\begin{bmatrix}A_{1}^{ii} & A_{1}^{ij} & {- B_{1}^{ij}} & 0 \\A_{1}^{ji} & A_{1}^{jj} & {- B_{1}^{jj}} & 0 \\0 & A_{2}^{ij} & B_{2}^{ij} & A_{2}^{ii} \\0 & A_{2}^{jj} & B_{2}^{jj} & A_{2}^{ji}\end{bmatrix}\begin{Bmatrix}p_{1}^{i} \\p^{j} \\v^{j} \\p_{2}^{i}\end{Bmatrix}} = {\begin{bmatrix}B_{1}^{ii} & 0 \\B_{1}^{ji} & 0 \\0 & B_{2}^{ii} \\0 & B_{2}^{ji}\end{bmatrix}\begin{Bmatrix}v_{1}^{i} \\v_{2}^{i}\end{Bmatrix}}} & (15)\end{matrix}$Using equation (15), one can define the Acoustic Transfer Vectors forthe global system: $\begin{matrix}{p = {\left\{ {atv} \right\}^{T}\begin{Bmatrix}v_{1}^{i} \\v_{2}^{i}\end{Bmatrix}}} & (16)\end{matrix}$and similarly derive the Acoustic Transfer Matrix [ATM] when theacoustic pressure has to be evaluated at different locations.Indirect Boundary Element Method (IBEM) Formulation

Using an indirect formulation, the acoustic pressure at any point of thedomain can be expressed in terms of single and double layer potentials[see A. D. Pierce, “Variational formulations in acoustic radiation andscattering”, Physical Acoustics XXII, 1993]: $\begin{matrix}{{p\left( \overset{\rightarrow}{x} \right)} = {{\int_{S}{{\mu\left( \overset{\rightarrow}{y} \right)}\frac{\partial{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{\partial n_{y}}{\mathbb{d}S_{y}}}} - {\int_{S}{{\sigma\left( \overset{\rightarrow}{y} \right)}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}{\mathbb{d}S_{y}}}}}} & (17)\end{matrix}$where σ({right arrow over (y)}) and μ({right arrow over (y)}) are thesingle and double layer potentials, respectively.

For the Neuman problem (i.e. structural velocity boundary condition) andwhen both sides of the boundary have the same velocity (i.e. thinshell), this equation can be expressed only in terms of double layerpotentials: $\begin{matrix}{{p\left( \overset{\rightarrow}{x} \right)} = {\int_{S}{{\mu\left( \overset{\rightarrow}{y} \right)}\frac{\partial{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{\partial n_{y}}{\mathbb{d}S_{y}}}}} & (18)\end{matrix}$Equation (18) can be evaluated on an arbitrary surface S′. It can bederived with respect to the normal at x ε S′, pre-multiplied by anadmissible test function δμ(x) and integrated over the surface S′:$\begin{matrix}{{\int_{S^{\prime}}{\frac{\partial{p\left( \overset{\rightarrow}{x} \right)}}{\partial n_{x}}{{\delta\mu}\left( \overset{\rightarrow}{x} \right)}{\mathbb{d}S^{\prime}}}} = {\int_{S^{\prime}}{\int_{S}{{\mu\left( \overset{\rightarrow}{y} \right)}\frac{\partial^{2}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{{\partial n_{x}}{\partial n_{y}}}{{\delta\mu}\left( \overset{\rightarrow}{x} \right)}{\mathbb{d}S_{y}}{\mathbb{d}S_{x}^{\prime}}}}}} & (19)\end{matrix}$Now, let the surface S′ tend to S and make use of the Euler equation:$\begin{matrix}{{- {\int_{S}{{j\omega\rho}\quad{v\left( \overset{\rightarrow}{x} \right)}{{\delta\mu}\left( \overset{\rightarrow}{x} \right)}{\mathbb{d}S}}}} = {\int_{S}{\int_{S}{{\mu\left( \overset{\rightarrow}{y} \right)}\frac{\partial^{2}{G\left( \overset{\rightarrow}{x} \middle| \overset{\rightarrow}{y} \right)}}{{\partial n_{x}}{\partial n_{y}}}{{\delta\mu}\left( \overset{\rightarrow}{x} \right)}{\mathbb{d}S_{y}}{\mathbb{d}S_{x}}}}}} & (20)\end{matrix}$After discretization using boundary elements, equation (18) becomes:p={d} ^(T){μ}  (21)Similarly, equation (20) becomes:[Q]{μ}=[H]{v _(b)}  (22)Combining equations (21) and (22):p={atv} ^(T) {v _(b)}  (23)where {atv} is the Acoustic Transfer Vector, given by:{atv} ^(T) ={d} ^(T) [Q] ⁻¹ [H]  (24)When the acoustic pressure is evaluated at several locations, equation(23) can be rewritten as:{p}=[ATM] ^(T) {v _(b)}  (25)where the Acoustic Transfer Matrix [ATM] is formed by the differentAcoustic Transfer Vectors.Finite/infinite Element Method (FEM/IFEM) Formulation

The solution of the Helmholtz equation based on a finite/infiniteelement approach leads to a system of linear equations:([K]+jpω[D]−ω ² [M]){p}=−jpω{F}  (26)where K is the fluid stiffness matrix, D is the fluid damping matrix, Mis the fluid mass matrix and F is the forcing vector, defined by:{F}=[C]{v _(b)}  (27)where C is a coupling matrix.

Combining equations (26) and (27),):{p}=[ATM] ^(T) {v _(b)}  (28)where the Acoustic Transfer Matrix [ATM] is given by: $\begin{matrix}{\lbrack{ATM}\rbrack^{T} = \frac{- {{j\rho\omega}\lbrack C\rbrack}}{\left( {\lbrack K\rbrack + {{j\rho\omega}\lbrack D\rbrack} - {\omega^{2}\lbrack M\rbrack}} \right)}} & (29)\end{matrix}$Finally, for each finite element grid point, the acoustic pressure canbe written as:p={atv} ^(T) {v _(b)}  (30)where {atv} is the Acoustic Transfer Vector, given by the correspondingrow of the [ATM]^(T) matrix.Use of the Reciprocity Principle

See F. Fahy, “The Reciprocity Principle and Applications inVibro-Acoustics”, Second International Congress on Recent Developmentsin air- and Structure Borne Sound and Vibration, 4-6 Mar. 1992, 591-598and/or K. R. Fyfe, L. Cremers, P. Sas, G. Creemers, “The use of acousticstreamlines and reciprocity methods in Automotive design sensitivitystudies”, Mechanical Systems and Signal Processing (1991) 5 (5),431-441.

An aspect of the present invention is the use of the reciprocityprinciple for efficiently computing the Acoustic Transfer Vectors. Asshown in equations (10), (15), (24) and (29), the evaluation of anyfield point related ATV requires the inversion of a matrix, whose orderis approximately equal to the number of nodes of the discretizedgeometry (mesh).

The numerical evaluation of the inverse of an order n matrix isperformed by solving a system of linear equations, whose right-hand-sideis built from the unity matrix, leading typically to one matrixfactorisation, and n back-substitution steps.[A][X]=[I]  (31)For large matrix orders, the computational effort and time required forperforming the n back-substitution steps is very significantly largerthan the factorisation time.

Looking to equation (10), it can be deduced that an ATV is a vector forwhich each coordinate corresponds to the pressure at the correspondingfield point due to a unit excitation (vibrating velocity) at onepoint/element on the surface, and no excitation elsewhere.$\begin{matrix}{{atv}_{i} = {\left\{ {atv} \right\}\begin{Bmatrix}0 \\\vdots \\1 \\\vdots \\0\end{Bmatrix}}} & (32)\end{matrix}$This is represented graphically in FIG. 4.

According to the reciprocity principle, the pressure response at a firstlocation due to an excitation at a second location is strictly equal tothe pressure response at the second location due to the same excitationat the first location. Therefore, if a source of strength Q₁ at position1 causes a pressure p₂ at position 2, and if a source of strength Q₂ atposition 2 causes a pressure p₁ at position 1, resulting in thefollowing relationship: $\begin{matrix}{{p_{1}Q_{1}} = {{p_{2}Q_{2}\quad{or}\quad\frac{p_{1}}{Q_{2}}} = \frac{p_{2}}{Q_{1}}}} & (33)\end{matrix}$Using the reciprocity principle to evaluate the ATV related to aspecific field point means that a monopole source (point source) ofstrength Q₁ should be positioned at the field point location 1, and thepressure is calculated on the boundary p₂. This is represented in FIG.5.

Equation 11 shows how the ATV will be exploited to convert the boundarysurface velocity (representing vibrations) into the field point acousticpressure. Since a structure may be complex, containing T-junctions andother discontinuities, surface vibrations are better defined onsurfaces, i.e. on finite elements, rather than at grid points (where thenormal directly is not always uniquely defined). Therefore, it isrequired to define element-based acoustic transfer vectors.

In the case where the source placed on the boundary (in 2) isdistributed over a small surface, equation (33) may be rewritten as:$\begin{matrix}{{p_{1}Q_{1}} = {\int_{S}{p_{2}v_{2}{\mathbb{d}S}}}} & (34)\end{matrix}$where v₂ is the source velocity. In the particular case where the sourceis distributed over a single element, the pressure at any point on thesurface can be approximated as:p ₂=(p ₂){N}  (35)where {N} is the interpolation function and (p₂) is the pressureevaluated at the element nodes. Similarly the source velocity can beapproximated as:v ₂=(N){v ₂}  (36)where {v₂} is the source velocity at the element nodes. Equations (34)to (36) lead to the following relation:p ₁ Q ₁=(p ₂)[C _(e) ]{v ₂}  (37)where [C_(e)] is the element coupling matrix defined as:[C _(e)]=∫_(S) _(e) {N}(N)dS  (38)For a monopole source, the source strength is given by: $\begin{matrix}{Q_{1} = {\frac{4\pi}{j\rho\omega}A}} & (39)\end{matrix}$where A is the monopole source amplitude. Combining (37) and (39):$\begin{matrix}{p_{1} = {\frac{j\quad\rho\quad\omega}{4\pi\quad A}{\left\langle p_{2} \right\rangle\left\lbrack C_{e} \right\rbrack}\left\{ v_{2} \right\}}} & (40)\end{matrix}$which can be rewritten as:p ₁ =[ATV _(e) ]{v ₂}  (41)where [ATV_(e)] is the element-based acoustic transfer vector, computedby: $\begin{matrix}{\left\lbrack {ATV}_{e} \right\rbrack = {\frac{j\quad{\rho\omega}}{4\pi\quad A}{\left\langle p_{2} \right\rangle\left\lbrack C_{e} \right\rbrack}}} & (42)\end{matrix}$Applying at the field point a monopole source with a unit amplitude (A=1and ω=2πf, we finally obtain the following expression for evaluating theelement-based acoustic transfer vector:$\begin{matrix}{\left\lbrack {ATV}_{e} \right\rbrack = {\frac{{j\rho}\quad f}{2}{\left\langle p_{2} \right\rangle\left\lbrack C_{e} \right\rbrack}}} & (43)\end{matrix}$showing that the ATV related to a given field point can then be computedfrom the boundary sound pressure values, correctly scaled.

The use of the reciprocity principle for evaluating the ATV's leads totwo fundamental advantages:

-   1. The ATV's can be directly computed on an element basis, removing    the ambiguity inherent to nodal values, in case of sharp edges and    T-junctions, where the normal vector is not uniquely defined.-   2. The ATV related to a given field point can then be computed with    a single excitation vector, representing the monopole source    excitation at the field point. This leads to a single back    substitution step. Since the number of field points (microphone    locations) is usually several orders of magnitude lower than the    number of boundary nodes, this results in tremendous gains in    computational effort.    Interpolation Technique

In the case of sound wave propagation in an open space, the fluid domaindoes not exhibit any resonant behaviour. The sound field is fullydetermined by various wave mechanisms, such as reflection by solidobjects, absorption on damping surfaces, diffraction around edge andwave interference. Therefore, for non-resonant media, Acoustic TransferVectors are rather smooth functions of the frequency, and ATVcoefficients can be accurately evaluated at any intermediate frequency,called a slave frequency, using a mathematical interpolation scheme,based on a discrete number of frequencies, called master frequencies. Itis important to note that the structural vibrations cannot be similarlyinterpolated, since these are directly dependent on the highly resonantdynamic behaviour of any structure (vibration mode shapes).

At least two interpolation mechanisms can be used:

-   1. A polynomial interpolation scheme such as a linear interpolation    scheme (see FIG. 6);-   2. A spline interpolation scheme such as a cubic spline scheme (see    FIG. 7), which is particularly well suited for approximating ATV's    (De Boor, C. A Practical Guide to Splines, Springer-Verlag, N.Y.,    1978).

Other interpolation schemes can be used, e.g. stochastic interpolation(Kriging interpolation).

The use of an interpolation scheme for evaluating the ATV's leads to thefollowing fundamental advantages:

-   1. It allows to build a complete frequency dependant ATV, with a    very limited number of frequency lines to be computed. In order to    build a complete frequency response with a traditional approach, the    number of frequency lines to be computed is usually over a hundred.    Using an interpolation mechanism, only a few master frequency lines    needs to be explicitly computed, any other frequency being    interpolated. The gain in computing time is usually over an order of    magnitude.-   2. Similarly, the ATV's have to be stored in a file database in    order to be further exploited. For instance they may be stored in    non-volatile memory of a computer system such as a disk or in mass    storage or for example on a CD-ROM. The interpolation mechanism    allows storage of only the master frequency ATV's in the database.    The corresponding vector at any intermediate frequency may then be    directly evaluated at a neglectible processing cost, and therefore    does not need to be stored in the database. The gain in disk space    is usually over an order of magnitude.-   3. For some specific applications, such as automotive powertrains,    the acoustic performance has to be evaluated for many different    operational conditions (e.g. different rpm's), each of these having    a different frequency contents. Using the ATV interpolation    mechanism, the same set of master frequencies can be used to build a    unique basis of ATV's, which are then interpolated and combined with    the structural response corresponding to any load case, at any    intermediate frequency needed for the specific operational    condition.    Inverse Numerical Acoustics

Equations (11) and (25) are the basic relations for the inversenumerical acoustics theory. The sound pressure is measured at a largenumber of microphone (field points) and the boundary velocity can beobtained using the relationship:{v _(b) }=[ATM] ⁻¹ {p}  (44)However, the inversion of the acoustic transfer matrix is not obvious,because the matrix is generally not square but rectangular and becauseit involves a Fredholm equation (of the first kind for the indirectapproach and of the second kind for the direct approach) and is illconditioned. Therefore the matrix inversion is preferably performedusing the singular value decomposition (SVD) technique, which allows thesolution of singular or close to singular systems. It is based on thefact that any n×m complex matrix can be written as:[ATM]=[V][σ][U] ^(H)  (45)where the superscript H stands for ‘transpose complex conjugate’, [σ] isa diagonal min(n,m)×min(n,m) real matrix, [U] is a m×min(n,m) complexmatrix and [V] is a n×min(n, m) complex matrix. The coefficients of [σ],called singular values, are stored in an decreasing order and matrices[U] and [V] are such that:[V] ^(H) [V]=[U] ^(H) [U]=[I]  (46)From equations (45) and (46) it follows:[ATM] ⁻¹ =[U][σ] ⁻¹ [V] ^(H)  (47)Nevertheless, singular or ill-conditioned matrices contain null or smallsingular values. This results in infinite or very large values in [σ]⁻¹.Whereas the infinite terms clearly lead to an infinite solution, thevery large values lead to a solution of equation (44) that will be verysensitive to the right hand side variations. Therefore, small errors onthe RHS will result in very large errors in the solution. To avoid thisproblem, the small or null terms of [σ] are set to zero in [σ]⁻¹. Thisprocess is called truncated singular value decomposition. The singularvalues are set to zero as soon as σ_(i)<ασ_(l) where α is a toleranceparameter.Panel Contribution Analysis

Panel Contribution Analysis is a fundamental engineering tool to guidethe product refinement in the development process. It is shownschematically in FIG. 8 in which contributions reaching the ear ofperson in a vehicle come from different parts or panels of the vehicle.Equations (9), (16), (23) or (30) can be rewritten as: $\begin{matrix}{p = {{\sum\limits_{e = 1}^{ne}p_{e}} = {\sum\limits_{e = 1}^{ne}{\left\lbrack {ATV}_{e} \right\rbrack^{T}\left\{ v_{e} \right\}}}}} & (48)\end{matrix}$where ne is the total number of elements. Subsequently, the contributionof a panel is given by the summation of element contributions over thepanel elements: $\begin{matrix}{p_{c} = {{\sum\limits_{pe}p_{e}} = {\sum\limits_{pe}{\left\lbrack {ATV}_{e} \right\rbrack^{T}\left\{ v_{e} \right\}}}}} & (49)\end{matrix}$where pe stands for panel elements.Modal ATV

The engineering process to compute the structural velocity {V_(b)} on avibrating surface relies usually on the structural finite elementmethod, and often on a modal superposition approach, where thestructural response is expressed as a linear combination of the modeshapes of the body:{v _(b)}=[Φ_(n) ]{mpf}  (50)Where [Φ_(n)] is the matrix composed of the modal vectors, projected onthe normal direction to the boundary surface, and {mpf} are the modalparticipation factors, also called the modal response of the structuralmodel, at a given excitation frequency. The term “mode” relates not onlyto natural or “eigen-” frequencies but also to operational frequenciessuch as defined by Ritz vectors.

Combining (50) with Equations (9), (16), (23) or (30) leads to:p={atv} ^(T)[Φ_(n) ]{mpf}  (51)where{atv} ^(T)[Φ_(n) ]={matv} ^(T)  (52)is called the Modal Acoustic Transfer Vector, which can be directlycombined with the modal response to give the sound pressure at a fieldpoint:p={matv} ^(T) {mpf}  (53)The concept of Modal Acoustic Transfer Vectors can be extended to anypossible deformation shapes of the body, so-called Ritz vectors. This isespecially interesting in the case of inverse numerical acoustics, wherethe unknown becomes then the modal participation factors.Optimisation Strategy

An embodiment of the present invention includes a method that allows thenumerical acoustic radiation prediction calculation to be extremelyfast, the main computational intensive task (calculation of the ATV's)being done as a pre-processing step. Therefore, it is directly possibleand practical to integrate the acoustic radiation prediction within anoptimisation loop, where the objective function is the acousticperformance (sound pressure levels, or radiated power according to theISO3744-1981 procedure), and where the design variables are eitherstructural or acoustic design variables.

An optimisation process in accordance with an embodiment of the presentinvention is shown at FIG. 9 a. The optimisation process will normallybe carried out on a digital computing system. It will typically combinea structural dynamic finite element solver (step 104) together with anATV-based acoustic prediction tool (step 106). In step 102 a set ofATV's is evaluated for the structure to be analysed using, for example,the reciprocity principle as described above. In step 104 a solver isused to determine the surface vibration velocities of the structure.Commercially available solvers are, for example, MSC.Nastran from MSCSoftware, USA, ANSYS from Ansys Inc. USA, ABAQUS from HKS Inc. In step106 the ATV's are combined with the surface velocities to determine anacoustic signature at one or more field points. As part of this processan ATV interpolation step (108) may optionally be used to increase thenumber of available ATV's.

The achieved performance is compared in step 110 with a desiredperformance or with a previously calculated performance to determine ifa desired or optimum performance is achieved. If not, a design changecan be made in step 112, e.g. add or remove stiffening elements to thestructure, change a dimension of the structure or a material (e.g. toprovide more or less damping). Provided these changes are relativelyminor there will be no appreciable change in the ATV's and thereforestep 102 does not need to be repeated. Instead the vibration response isrecalculated in step 104 and a new performance analysis carried out.Avoiding the re-calculation of the ATV's is a significant advantage ofthis embodiment.

A similar methodology is shown in FIG. 9 b using MATV's. In this casestep 106 is replaced with a step 116 of obtaining the MATV's byprojecting the ATV's determined in step 102 into a co-ordinate systemdefined by the vibrational modes determined in step 114. The modes usedmay be natural modes, e.g. the shapes of the structure determined by thenatural or eigen-frequencies of the structure, or the modes may beoperational modes, e.g. those determined by Ritz vectors. An optionalinterpolation step 118 may be used to generate MATV's at intermediatefrequencies. The response at one or more field points is calculated fromthe MATV's in step 120 in which the results are compared with apreviously calculated result or with a desired result. If unsatisfactorya design change may be made in step 122 and re-evaluated in steps114-120.

Implementation

The methods of the present invention may be implemented on a processingengine such as a workstation or a personal computer. The processingengine may be a server accessible via a telecommunications network suchas a LAN, a WAN, the Internet, an Intranet. The server may be adapted tocarry out any of the methods of the present invention, for example adescriptor file of a body may be entered at a near terminal andtransmitted to the server via the Internet. The server then carries outone of the methods of the present invention and returns to a nearlocation e.g. an e-mail box, any response of any of the methods inaccordance with the present invention. Such a response may be, forinstance, an ATV, a vibrational amplitude such as an acoustic pressurelevel, a surface vibration of the body, a revised design of at least apart of the body.

By way of example only and with reference to FIG. 10, in one embodimenta near terminal 12 which communicates with a server 14 via acommunications network 16 such as the Internet, or an Intranet.Information about a body to be analyzed or assessed is entered into aninput 18 at the near terminal 12, e.g. in the form of a representationof the body and coordinates of a reference point. This is communicatedto the server 14 which performs one or more methods of the invention andprovides to an output 20 of the near terminal 12 a response inaccordance with the methods described above. The server 14 operates inconjunction with a computer program which implements the invention andwhich is stored on a data carrier 22 which is accessible to the server14.

The methods of the present invention may be implemented as computerprograms which may be stored on data carriers such as diskettes orCD-ROMS. These programs may also be downloaded via the Internet or anyother telecommunications network.

FIG. 11 is a schematic representation of a computing system which can beutilized with the methods and in a system according to the presentinvention. A computer 10 is depicted which may include a video displayterminal 14, a data input means such as a keyboard 16, and a graphicuser interface indicating means such as a mouse 18. Computer 10 may beimplemented as a general purpose computer, e.g. a UNIX workstation.

Computer 10 includes a Central Processing Unit (“CPU”) 15, such as aconventional microprocessor of which a Pentium III processor supplied byIntel Corp. USA is only an example, and a number of other unitsinterconnected via system bus 22. The computer 10 includes at least onememory. Memory may include any of a variety of data storage devicesknown to the skilled person such as random-access memory (“RAM”),read-only memory (“ROM”), non-volatile read/write memory such as a harddisc as known to the skilled person. For example, computer 10 mayfurther include random-access memory (“RAM”) 24, read-only memory(“ROM”) 26, as well as an optional display adapter 27 for connectingsystem bus 22 to an optional video display terminal 14, and an optionalinput/output (I/O) adapter 29 for connecting peripheral devices (e.g.,disk and tape drives 23) to system bus 22. Video display terminal 14 canbe the visual output of computer 10, which can be any suitable displaydevice such as a CRT-based video display well-known in the art ofcomputer hardware. However, with a portable or notebook-based computer,video display terminal 14 can be replaced with a LCD-based or a gasplasma-based flat-panel display. Computer 10 further includes userinterface adapter 19 for connecting a keyboard 16, mouse 18, optionalspeaker 36, as well as allowing optional physical value inputs fromphysical value capture devices such as sensors 40 of an external system20. The sensors 40 may be any suitable sensors for capturing physicalparameters of system 20. These sensors may include any sensor forcapturing relevant physical values required for solution of the problemsaddressed by the present invention Such sensors can be microphones andaccelerometers (for acoustics). Additional or alternative sensors 41 forcapturing physical parameters of an additional or alternative physicalsystem 21 may also connected to bus 22 via a communication adapter 39connecting computer 10 to a data network such as the Internet, anIntranet a Local or Wide Area network (LAN or WAN) or a CAN. This allowstransmission of physical values or a representation of the physicalsystem to be simulated over a telecommunications network, e.g. enteringa description of a physical system at a near location and transmittingit to a remote location, e.g. via the Internet, where a processorcarries out a method in accordance with the present invention andreturns a parameter relating to the physical system to a near location.

The terms “physical value capture device” or “sensor” includes deviceswhich provide values of parameters of a physical system to be simulated.Similarly, physical value capture devices or sensors may include devicesfor transmitting details of evolving physical systems. The presentinvention also includes within its scope that the relevant physicalvalues are input directly into the computer using the keyboard 16 orfrom storage devices such as 23.

A parameter control unit 37 of system 20 and/or 21 may also be connectedvia a communications adapter 38. Parameter control unit 37 may receivean output value from computer 10 running a computer program fornumerical analysis in accordance with the present invention or a valuerepresenting or derived from such an output value and may be adapted toalter a parameter of physical system 20 and/or system 21 in response toreceipt of the output value from computer 10. For example, a dimensionof the body or structure to be simulated may be altered, a material maybe changed, a stiffening or dampening element may be added or removed.

Computer 10 also includes a graphical user interface that resides withinmachine-readable media to direct the operation of computer 10. Anysuitable machine-readable media may retain the graphical user interface,such as a random access memory (RAM) 24, a read-only memory (ROM) 26, amagnetic diskette, magnetic tape, or optical disk (the last three beinglocated in disk and tape drives 23). Any suitable operating system andassociated graphical user interface (e.g., Microsoft Windows) may directCPU 15. In addition, computer 10 includes a control program 51 whichresides within computer memory storage 52. Control program 51 containsinstructions that when executed on CPU 15 carry out the operationsdescribed with respect to any of the methods of the present invention.

Those skilled in the art will appreciate that the hardware representedin FIG. 11 may vary for specific applications. For example, otherperipheral devices such as optical disk media, audio adapters, or chipprogramming devices, such as PAL or EPROM programming devices well-knownin the art of computer hardware, and the like may be utilized inaddition to or in place of the hardware already described.

In the example depicted in FIG. 11, the computer program product (i.e.control program 51) can reside in computer storage 52. However, it isimportant that while the present invention has been, and will continueto be, that those skilled in the art will appreciate that the mechanismsof the present invention are capable of being distributed as a programproduct in a variety of forms, and that the present invention appliesequally regardless of the particular type of signal bearing media usedto actually carry out the distribution. Examples of computer readablesignal bearing media include: recordable type media such as floppy disksand CD ROMs and transmission type media such as digital and analoguecommunication links.

While the invention has been shown and described with reference topreferred embodiments, it will be understood by those skilled in the artthat various changes or modifications in form and detail may be madewithout departing from the scope and spirit of this invention.

1. A method for computing a Wave Transfer Vector from a surface point ona body to a reference position remote from the body based on thereciprocity principle, comprising the steps of: simulating positioningof a monopole, omnidirectional wave energy source at the referenceposition remote from the body; computing a boundary oscillationamplitude of the wave generated by the source at a surface of the body;and deriving from the boundary oscillation amplitude said Wave TransferVector.
 2. The method of claim 1 wherein the computing step is carriedout by a numerical method.
 3. The method according to claim 2 whereinthe numerical method is one of: a finite element method, a combinationof the finite and infinite element methods, a direct boundary elementmethod, a direct multi-domain boundary element method, a indirectboundary element method.
 4. A processing engine adapted to carry out themethod of claim
 2. 5. A computer program product for executing on acomputer, the computer program product executing the method steps ofclaim 2 when executed on the computer.
 6. A method of inputting at anear terminal a representation of a body and coordinates of a referencepoint and transmitting these to a remote terminal running a program forexecuting the method of claim 2, and receiving at a near location anoutput of any of the methods.
 7. The method according to claim 1,wherein wave source is an acoustic source.
 8. The method according toclaim 1 further comprising a step of computing an additional WaveTransfer Vector comprising: computing at least a first and a second wavetransfer vector at a first and a second predetermined frequency,respectively, and computing the additional Wave Transfer Vector at afrequency intermediate the first and second frequency by interpolationbetween the first and second Wave Transfer Vectors.
 9. The method ofclaim 8 wherein the interpolation technique is one of a polynomialinterpolation mechanism and a spline interpolation mechanism.
 10. Themethod according to claim 1 wherein the Wave Transfer Vector is anAcoustic Transfer Vector, further comprising the step of computing aModal Acoustic Transfer Vector (MATV) from an acoustic transfer vector(ATV) in an alternative coordinate system defined by a set of deformedshapes of a body, comprising: projecting the ATV into the alternativecoordinate system.
 11. The method of claim 10 further comprising thestep of: using the MATV to predict a response of the body or the effectof such a response at a reference point remote from the body.
 12. Aprocessing engine adapted to carry out the method of claim
 1. 13. Acomputer program product for executing on a computer, the computerprogram product executing the method steps of claim 1 when executed onthe computer.
 14. A method of inputting at a near terminal arepresentation of a body and coordinates of a reference point andtransmitting these to a remote terminal running a program for executingthe method of claim 1, and receiving at a near location an output of anyof the methods.
 15. The method according to claim 14, wherein the outputis one of: an ATV, an oscillation amplitude such as an acoustic pressurelevel, a surface vibration of the body, a revised design of at least apart of the body.
 16. A computer system for computing a Wave TransferVector from a surface point on a body to a reference position remotefrom the body based on the reciprocity principle, comprising: means forsimulating positioning of a monopole, omnidirectional wave energy sourceat the reference position remote from the body; means for computing aboundary oscillation amplitude of the wave generated by the source at asurface of the body; and means for deriving from the boundaryoscillation amplitude said Wave Transfer Vector.
 17. The computer systemaccording to claim 16, further comprising means for computing anadditional Wave Transfer Vector at a frequency intermediate a first andsecond frequency by interpolation between a first and a second WaveTransfer Vector at the first and second frequencies.
 18. The computersystem according to claim 17, wherein the Wave Transfer Vector is anAcoustic Transfer Vector, further comprising: means for computing aModal Acoustic Transfer Vector (MATV) from an acoustic transfer vector(ATV) in an alternative coordinate system defined by a set of deformedshapes a body by projecting the ATV into the modal space.
 19. Thecomputer system according to claim 16, wherein the Wave Transfer Vectoris an Acoustic Transfer Vector, further comprising: means for computinga Modal Acoustic Transfer Vector (MATV) from an acoustic transfer vector(ATV) in an alternative coordinate system defined by a set of deformedshapes a body by projecting the ATV into the modal space.